A New Ensemble HDG Method for Parameterized Convection Diffusion PDEs

A New Ensemble HDG Method for Parameterized Convection Diffusion PDEs

Year:    2021

Author:    Liangya Pi, Yong Yu, Yangwen Zhang, Gang Chen, Liangya Pi, Yangwen Zhang

Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 1 : pp. 144–175

Abstract

A new second order time stepping ensemble hybridizable discontinuous Galerkin method for parameterized convection diffusion PDEs with various initial and boundary conditions, body forces, and time depending coefficients is developed. For ensemble solutions in $L^∞$($0$, $T$; $L^2$($Ω$)), a superconvergent rate with respect to the freedom degree of the globally coupled unknowns for all the polynomials of degree $k$ ≥ $0$ is established. The results of numerical experiments are consistent with the theoretical findings.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2019-0190

Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 1 : pp. 144–175

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    32

Keywords:    HDG method ensemble methods parameterized convection diffusion PDEs numerical analysis.

Author Details

Liangya Pi

Yong Yu

Yangwen Zhang

Gang Chen

Liangya Pi

Yangwen Zhang

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